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  • A committee of 6 people needs to be selected from a group of 10 individuals, including 4 men and 6 women. If at least 3 men must be on the committee, how many different c

A committee of 6 people needs to be selected from a group of 10 individuals, including 4 men and 6 women. If at least 3 men must be on the committee, how many different committees can be formed?

 

Option: 1

1


Option: 2

3


Option: 3

2


Option: 4

0


Answers (1)

best_answer

To calculate the number of different committees that can be formed, where at least 3 men must be on the committee, we can consider different scenarios based on the number of men on the committee.

Case 1: Selecting 3 men and 3 women:

The number of ways to select 3 men from 4 men is given by\mathrm{ C(4,3)=4}

The number of ways to select 3 women from 6 women is given by \mathrm{ C(6,3)=20.}

The total number of committees in this case is \mathrm{ 4 \times 20=80}. Case 2 : Selecting 4 men and 2 women:

The number of ways to select 4 men from 4 men is given by \mathrm{ C(4,4)=1}

The number of ways to select 2 women from 6 women is given by \mathrm{C(6,2)=15}

The total number of committees in this case is \mathrm{1 \times 15=15.}

Case 3: Selecting all 6 men:

The number of ways to select 6 men from 4 men is given by \mathrm{C(4,6),} which is not possible as there are only 4 men available.

Therefore, there are no committees that satisfy the condition of selecting at least 3 men.

Hence, there are 0 different committees that can be formed where at least 3 men must be on the committee.

 

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SANGALDEEP SINGH

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